GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 25 Jan 2020, 02:33

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If xy < zy < 0, is y positive? 1. x < z 2. x is negative

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 12 Aug 2015
Posts: 279
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

### Show Tags

08 Jan 2016, 09:41
17
00:00

Difficulty:

65% (hard)

Question Stats:

53% (01:30) correct 47% (01:28) wrong based on 252 sessions

### HideShow timer Statistics

If xy < zy < 0, is y positive?

(1) x < z
(2) x is negative
##### Most Helpful Expert Reply
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10011
Location: Pune, India
Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

### Show Tags

08 Jan 2016, 23:48
8
3
shasadou wrote:
If xy < zy < 0, is y positive?

(1) x < z
(2) x is negative

xy < zy < 0
Both xy and zy are negative.
Either y is negative, x and z both are positive and x > z.
Or y is positive, x and z both are negative and x < z.

Question: Is y positive?

(1) x < z
If x < z, x and z are both negative and y is positive. Sufficient.

(2) x is negative
If x is negative, z is also negative and then y must be positive. Sufficient.

Answer (D)
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
##### Most Helpful Community Reply
CEO
Joined: 20 Mar 2014
Posts: 2548
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

### Show Tags

08 Jan 2016, 09:50
5
3
shasadou wrote:
If xy < zy < 0, is y positive?

(1) x < z
(2) x is negative

Typical inequalities question where a step by step method is a must in order to reach the correct answer.

You are given xy<zy ---> y(x-z)<0 , 2 cases possible here

1. y<0 and x>z
2. y>0 and x<z

The question is asking us whether y >0

Per statement 1, x<z ---> case 2 comes into the picture, providing a definite answer to the question asked. Sufficient.

Per statement 2, x< 0 ---> use the given information that xy<0 --> y must be >0 for xy<0 with x<0. Thus sufficient as well.

Both statements are sufficient ----> D is the correct answer.

Hope this helps.
##### General Discussion
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4226
Location: Canada
Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

### Show Tags

20 Feb 2019, 09:47
1
Top Contributor
shasadou wrote:
If xy < zy < 0, is y positive?

(1) x < z
(2) x is negative

Target question: Is y positive?

Given: xy < zy < 0,
Let's focus on this part of the inequality: xy < zy
Subtract xy from both sides to get: 0 < zy - xy
Factor out the y to get: 0 < y(z - x) (this will come in handy later)

Statement 1: x < z
Subtract x from both sides to get: 0 < z - x
In other words, (z - x) is POSITIVE
This means we can take our given inequality 0 < y(z - x) and divide both sides by (z - x) to get: 0 < y
So, the answer to the target question is YES, y IS positive
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x is negative
The given information tells us that xy < zy < 0
This means xy < 0
In other words, xy is NEGATIVE
So, if x is negative, then it MUST be the case that y is POSITIVE
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

RELATED VIDEO FROM MY COURSE

_________________
Test confidently with gmatprepnow.com
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

### Show Tags

10 Jan 2016, 19:13
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If xy < zy < 0, is y positive?

(1) x < z
(2) x is negative

When you modify the original condition and the question, it becomes (x-z)y<0에서 y>0? --> x-z<0?. x<Z에서 1) is yes, which is sufficient.
For 2), if x<0, y>0 derived from xy<0, which is yes and sufficient. Therefore, the answer is D.

 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Intern
Joined: 25 Jun 2013
Posts: 10
Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

### Show Tags

12 Jun 2016, 15:54
Can you just divide the original equation by Y?
XY < ZY < 0 --> X< Z < 0?

If not, why not?
CEO
Joined: 20 Mar 2014
Posts: 2548
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

### Show Tags

12 Jun 2016, 16:21
1
glochou wrote:
Can you just divide the original equation by Y?
XY < ZY < 0 --> X< Z < 0?

If not, why not?

Dividing an inequality by a variable whose sign is UNKNOWN is the biggest mistake you can make in inequality questions.

The sign of the inequality changes if you divide or multiply by a negative number. This is the reason why you CAN NOT divide by y.

If xy<zy ---> y*(x-z)<0 --> this means that either

Case 1: y>0 and x-z<0 OR
Case 2: y<0 and x-z>0

When you divide by y WITHOUT reversing the signs, you are inherently assuming that y>0. This is the very question asked.
Intern
Joined: 18 Nov 2013
Posts: 45
If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

### Show Tags

23 Jul 2018, 11:44
KarishmaB wrote:
shasadou wrote:
If xy < zy < 0, is y positive?

(1) x < z
(2) x is negative

xy < zy < 0
Both xy and zy are negative.
Either y is negative, x and z both are positive and x > z.
Or y is positive, x and z both are negative and x < z.

Question: Is y positive?

(1) x < z
If x < z, x and z are both negative and y is positive. Sufficient.

(2) x is negative
If x is negative, z is also negative and then y must be positive. Sufficient.

Answer (D)

as per the question, it asks y(x-z)<0;
I agree for option 1 is sufficient on the basis that x<z;
for the second option, since x is -ve
x=-5 and z=-4 then y(-5-(-4))<0; hence y is +ve
x=-5 and z=-10 then y(-5-(-10))<0; here y should be -ve

there are conflicting solutions whether y is +ve/-ve

where am I wrong??
Director
Joined: 14 Dec 2017
Posts: 505
Location: India
Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

### Show Tags

23 Jul 2018, 11:54
harish1986 wrote:
KarishmaB wrote:
shasadou wrote:
If xy < zy < 0, is y positive?

(1) x < z
(2) x is negative

xy < zy < 0
Both xy and zy are negative.
Either y is negative, x and z both are positive and x > z.
Or y is positive, x and z both are negative and x < z.

Question: Is y positive?

(1) x < z
If x < z, x and z are both negative and y is positive. Sufficient.

(2) x is negative
If x is negative, z is also negative and then y must be positive. Sufficient.

Answer (D)

as per the question, it asks y(x-z)<0;
I agree for option 1 is sufficient on the basis that x<z;
for the second option, since x is -ve
x=-5 and z=-4 then y(-5-(-4))<0; hence y is +ve
x=-5 and z=-10 then y(-5-(-10))<0; here y should be -ve

there are conflicting solutions whether y is +ve/-ve

where am I wrong??

From Statement 2, we don't get any information for z & we are not bothered about z, all we need to figure out is whether y > 0

We know from question prompt that xy < 0, hence if x < 0, then y > 0

I hope that helps

Thanks,
GyM
_________________
Director
Joined: 14 Dec 2017
Posts: 505
Location: India
Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

### Show Tags

23 Jul 2018, 11:56
harish1986 wrote:
KarishmaB wrote:
shasadou wrote:
If xy < zy < 0, is y positive?

(1) x < z
(2) x is negative

xy < zy < 0
Both xy and zy are negative.
Either y is negative, x and z both are positive and x > z.
Or y is positive, x and z both are negative and x < z.

Question: Is y positive?

(1) x < z
If x < z, x and z are both negative and y is positive. Sufficient.

(2) x is negative
If x is negative, z is also negative and then y must be positive. Sufficient.

Answer (D)

as per the question, it asks y(x-z)<0;
I agree for option 1 is sufficient on the basis that x<z;
for the second option, since x is -ve
x=-5 and z=-4 then y(-5-(-4))<0; hence y is +ve
x=-5 and z=-10 then y(-5-(-10))<0; here y should be -ve

there are conflicting solutions whether y is +ve/-ve

where am I wrong??

The #'s plugged in are not correct x < z, hence x=-5 and z=-10 is not valid
_________________
Intern
Joined: 11 Jun 2015
Posts: 18
Location: Iran (Islamic Republic of)
Concentration: Accounting, Finance
WE: Education (Education)
Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

### Show Tags

03 Sep 2018, 04:20
xy<zy<0
1: x<z, then -x>-z, if we subtract it from above inequality we will get y>0
2: because xy<0 and x<0, therefore y>0
Manager
Joined: 20 Oct 2018
Posts: 220
GMAT 1: 690 Q49 V34
GMAT 2: 740 Q50 V40
Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

### Show Tags

18 Nov 2019, 05:17
Official explanation

Solution: D

This difficult inequality problem requires that you properly leverage the information from the question stem. The second statement is relatively easy so you should start there – if x is negative and xy is negative then y must be positive. The second statement is sufficient. Since the second statement is relatively straightforward you should expect the 1st statement to be harder: from the question stem you know that xy < zy. If y were positive then you could divide by y and see that x < z. If y were negative then you could divide both sides to see that x > z. Since statement 1 proves that x < z then it must be the first case and y must be positive. Answer is D. Number picking is awkward and time consuming on first statement so don’t forget to use algebra as your first approach in any inequality problem.
Manager
Joined: 30 Oct 2019
Posts: 95
Location: United Kingdom
Concentration: General Management, Technology
GPA: 4
Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative  [#permalink]

### Show Tags

01 Dec 2019, 12:55
xy<zy<0.

Tip 1: xy<zy, cancel y.. x<z.. dont do that. This is because you dont know what y is (positive or negative)

So, xy<zy,
or, xy-zy<0,
or, y(x-z)<0.

So, Either y<0, therefore in this case, (x-z)>0 .....(i)
OR, (x-z)<0, therefore in this case, y>0 ........(ii)

(1) x<z, which means (x-z)<0, which means equation (ii) is valid. y>0. SUFFICIENT
(2) x is negative, we know xy<0, if x negative, then y must be positive. SUFFICIENT

Answer: D
Re: If xy < zy < 0, is y positive? 1. x < z 2. x is negative   [#permalink] 01 Dec 2019, 12:55
Display posts from previous: Sort by

# If xy < zy < 0, is y positive? 1. x < z 2. x is negative

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne